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They indeed do become rarer. Plotting all the primes in a single row makes this apparent, like so: https://susam.net/primegrid.html#1-1-1000000 https://susam.ne
by susam 1y ago
They indeed do become rarer. Plotting all the primes in a single row makes this apparent, like so: https://susam.net/primegrid.html#1-1-1000000 https://susam.net/primegrid.html#1-1-1000000
In fact, according to the celebrated prime number theorem, the number of primes less than or equal to n is asymptotic to n/log n, which means the density of primes near n is asymptotic to 1/log n.
I have a small section about this at https://susam.net/journey-to-prime-number-theorem.html#prime-number-theorem https://susam.net/journey-to-prime-number-theorem.html#prime... if you want to read more about this.
See also: https://en.wikipedia.org/wiki/Prime_number_theorem https://en.wikipedia.org/wiki/Prime_number_theorem
- eru 1y agoYes. > In fact, according to the celebrated prime number theorem, the number of primes less than or equal to n is asymptotic to n/log n, which means the density of primes near n is asymptotic to 1/log n. When written down as a string of digits, log n is another way to say 'proportional to the number of digits'. The number of digits grows fairly slowly, thus also the 'probability' of a number being prime drops very slowly.